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2006 Schauder estimates, Harnack inequality and Gaussian lower bound for Kolmogorov-type operators in non-divergence form
Marco Di Francesco, Sergio Polidoro
Adv. Differential Equations 11(11): 1261-1320 (2006).

Abstract

We prove some Schauder-type estimates and an invariant Harnack inequality for a class of degenerate evolution operators of Kolmogorov type. We also prove a Gaussian lower bound for the fundamental solution of the operator and a uniqueness result for the Cauchy problem. The proof of the lower bound is obtained by solving a suitable optimal control problem and using the invariant Harnack inequality.

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Marco Di Francesco. Sergio Polidoro. "Schauder estimates, Harnack inequality and Gaussian lower bound for Kolmogorov-type operators in non-divergence form." Adv. Differential Equations 11 (11) 1261 - 1320, 2006.

Information

Published: 2006
First available in Project Euclid: 18 December 2012

zbMATH: 1153.35312
MathSciNet: MR2277064

Subjects:
Primary: 35K65
Secondary: 35A08, 35K57

Rights: Copyright © 2006 Khayyam Publishing, Inc.

JOURNAL ARTICLE
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Vol.11 • No. 11 • 2006
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